Remarks on the solutions of the Maxwell- Chern-Simons theories

TL;DR

This paper investigates the large-distance behavior of Maxwell-Chern-Simons theories, revealing that the pure Chern-Simons limit is insufficient and exploring the properties of singular self-dual solutions in the coupled gauge-matter system.

Contribution

It demonstrates that the pure Chern-Simons limit does not capture the large-distance behavior and analyzes singular self-dual solutions in the coupled gauge-matter model.

Findings

Pure Chern-Simons limit does not describe large-distance behavior.

No regular self-dual solutions in the coupled model.

Existence of interesting singular self-dual solutions.

Abstract

The large distance behavior of the Maxwell- Chern-Simons (MCS) equations is analyzed, and it is found that the pure Chern-Simons limit, (when the Maxwell term is dropped from the equations), does not describe the large distance limit of the MCS model. This necessitates the solution of the original problem. The MCS gauge theory coupled to a nonrelativistic matter field, (governed by the gauged non-linear Schr\"odinger equation), is studied. It turns out, that there are no regular self-dual solutions as in the pure Chern-Simons case, but the model admits interesting, though singular self-dual solutions. The properties of these solutions, and their large distance limits are analyzed.